Defence giant BAE Systems has drafted in management consultants to examine the future of its historic shipyards in Glasgow and Portsmouth, creating fears that thousands of jobs could be at risk.

LEK Consulting is understood to be reviewing all potential options for the BAE Systems Surface Ships division, including shutting one of the three shipyards – there are two 19th-century sites very close to each other on the River Clyde in Scotland.

BAE will be keen to impress that the options have not been fully assessed, as it is already under fire for making 899 people redundant at its Brough plant in North Yorkshire, which manufactures Hawk Advanced Jet Trainer.

The company has been forced to look at the future of the shipyards as the £5bn contract for two 65,000-tonne super-carrier warships draws to a close. The ships are due to launch in 2018 – most work would be completed sooner - and there are fears that subsequent Ministry of Defence programmes will not be enough to keep the yards' 7,000 employees busy.

An defence industry source said: "It looks like there would only be enough regular work for one shipyard [the Glasgow bases or Portsmouth] from three or four years time."

However, LEK is also thought to be looking at internationalising the business to help BAE win work overseas. Alternatively, the MoD could step in and help fund the yards.

The source ruled out a straight sale as a likely option. He said: "Who would buy them? There's no one to sell it to [in the current market]."

LEK's thinking could be muddied if Scottish First Minister Alex Salmond pushes ahead with a referendum on the nation's future. British warships are unlikely to be built in Scotland should Scots vote for independence.

However, a second source suggested there could be some hope with the forthcoming Type 26 Global Combat Ship programme. BAE is already designing the ships, which will be built at the rate of one per year from 2020.

The FTSE 100 company, led by chief executive Ian King, is no stranger to controversy. In 2010, BAE paid fines totalling nearly £286m in the UK and US, after pleading guilty to charges of imperfect accounting practices and false statements in relation to contracts in Tanzania and Saudi Arabia.

A BAE spokeswoman said: "LEK are working with us. We do bring in consultants to work with us from time to time. This is analytical modelling to support normal business planning activity."